Discrete port-Hamiltonian system model of a single-reed woodwind instrument

Champ Darabundit ^* Gary Scavone

• McGill University, Montreal, Canada

Time-domain simulation of woodwind instruments typically involves the development of separate discrete-time component models for the excitation mechanism --- the single beating reed -- and the resonator --- a horn with toneholes. Modelling of these components has largely been undertaken via digital waveguide (DWG) or finite-difference time-domain (FDTD) methods. We present a separate approach based on the modular and energy-based port-Hamiltonian system (PHS) framework. We recast each component of a woodwind instrument as a PHS model and incorporate novel elements in each derivation. In the beating reed model, we make use of recent work on energy quadratization to formulate an explicit scheme of the nonlinear Hunt-Crossley contact force coupled to a nonlinear Bernoulli flow. In the horn model, we discretize a distributed PHS of the horn equation with a general version of the symplectic St{\"o}rmer-Verlet scheme verifying previously proposed FDTD schemes. In the tonehole model, we propose a new low-frequency model of the tonehole and model transitions through a switching PHS. Finally, simulations are performed on a test instrument and the stability of the overall scheme is demonstrated.